Bryan Fiabema struck the only goal of the game at St George's Park.
"I'm really pleased with the performance, even if the margin of victory could and should have been greater," he told the official Chelsea website.
"For the first 35 minutes, we were excellent both with and without the ball. We were relentless with our press and created opportunities from that but we didn't take them and a team of Man United's quality are always going to have periods in the game where they threaten you.
"We spoke at half-time about not letting our frustrations spill over into poor decision-making and to avoid doing things that weren't part of the game plan. The goal obviously came at a great time and then we had opportunities to make it 2-0 and 3-0 but didn't take them so we had to ride out a little bit of a storm towards the end."
Brand was particularly impressed with the collective effort in recording their fifth consecutive clean sheet.
"If you're not conceding goals in games then you give yourselves an opportunity," he continued. "I know that's a cliché but it's also a fact. I always feel quite confident is us defending and the back three did that really well when they had to – the centre-halves put their heads on things and the goalkeeper came to claim the ball, which was really pleasing.
"We defended really well as a team. A lot of the good work we do comes from the front three and I thought Bryan Fiabema, Marcel Lewis and Myles Peart-Harris at the start really set the tone with their pressing, which helps the whole team defend from top to bottom."